SOLUTION: struggling with this 2t(x-2t)=y(x-y) find x in terms of t and y

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Question 182664: struggling with this
2t(x-2t)=y(x-y)
find x in terms of t and y
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
2t%28x+-+2t%29+=+y%28x+-+y%29
2tx+-+4t%5E2+=+xy+-+y%5E2
Get the x terms on one side by
subtracting xy from both sides
2tx+-+xy+-+4t%5E2+=+-y%5E2
Add 4t%5E2 to both sides
2tx+-+xy+=+4t%5E2+-+y%5E2
Factor out x from the left side
x%2A%282t+-+y%29+=+4t%5E2+-+y%5E2
x+=+%284t%5E2+-+y%5E2%29+%2F+%282t+-+y%29
I can factor the numerator. It is the difference of
two perfect squares like a%5E2+-+b%5E2+=+%28a+%2B+b%29%28a+-+b%29
x+=+%28%282t+%2B+y%29%282t+-+y%29%29+%2F+%282t+-+y%29
x+=+2t+%2B+y answer